Question

Help! Me ajuda por favor. Resolva usando a Regra de Cremer;

a) x+4y=0
3x+2y=5

b)5x-4y=6
-x+y=-1

Answer 1

Manfred,
Vamos passo a passo

Pela Regra de Cramer,
                                       x = Dx/D            y = Dy/D
     Onde
                   D = determinante do sistema
                   Dx, Dy = determinante da respectiva variável

As duas tem o mesmo procedimento de solução 
Vou resolver a primeira.
Conhecendo a metodologia, a outra leva poucos minutos

                   $D= \left[\begin{array}{ccc}1&&4\\&&\\3&&2\end{array}\right] =-10 \\ \\ Dx= \left[\begin{array}{ccc}0&&4\\&&\\5&&2\end{array}\right] =-20 \\ \\ Dy= \left[\begin{array}{ccc}1&&0\\&&\\3&&5\end{array}\right] =5$

                 x = -20/-10 = 2
                 y = 5/-10 = - 1/2
                                                   S = {2, -1/2}

Answer 2

$\left \{ {{5x-4y=6} \atop {-x+y=-1}} \right. \\\\\\ D = \left[\begin{array}{ccc}5&-4\\-1&1\end{array}\right] \to~~~~ D = [5*1]-[(-1)*(-4)]\to\\\\ D = 5-4\to~~~~ \boxed{D = 1}\\\\\\ D_x = \left[\begin{array}{ccc}6&-4\\-1&1\end{array}\right]\to~~~~ D_x = [6*1]-[(-1))*(-4)]\to\\\\ D_x = 6-4\to~~~~ \boxed{D_x = 2}\\\\\\ D_y= \left[\begin{array}{ccc}5&6\\-1&-1\end{array}\right] \to~~~~ D_y = [5*(-1)]-[-1*6]\to\\\\ D_y = -5+6\to~~~~ \boxed{D_y = 1}$



$x = \dfrac{D_x}{D} \to~~~~x = \dfrac{2}{1}\to~~~~\boxed{x=2} \\\\\\\\ y = \dfrac{D_y}{D} \to~~~~y = \frac{1}{1}\to~~~~\boxed{y =1}\\\\\\\\\\ \Large\boxed{\boxed{ S = \left\{ 2~~;~~1 \right\}}}$